The recognizer used in AsTeR captures logical structure
present in documents encoded in the TeX family of languages. An
important feature of this recognizer is that it works on the
entire gamut of encodings, ranging from plain ASCII documents,
i.e.,no explicit markup, up to documents containing
completely unambiguous encodings of the logical structure.

The basic document model used in AsTeR is the attributed
tree. Each hierarchical level of the document is modeled as a
node in this tree. Each node can have content, children and
attributes. Using object-oriented terminology, each different
kind of node of the tree is called an object. Thus,
``chapter'', ``section'', ``paragraph'', and ``sentence'' are
all objects. If a document contained five sections, its
representation in AsTeR would have five instances of object
``section''. This object-oriented terminology is used because
AsTeR actually uses CLOS objects in this fashion. The use of an
object-oriented language was instrumental in allowing us to
develop and implement the ideas in AsTeR incrementally and
effectively.

This attributed tree structure is augmented to represent
mathematical content; we call this augmented representation the
quasi-prefix form, (see figure fig:math-object).
Expressions that are completely unambiguous,
e.g.,[tex2html_wrap313], are captured in their prefix
form. In addition to linearizing the underlying tree structure,
mathematical notation uses visual attributes/ such as
superscripts and subscripts, whose interpretation is
context-dependent. We extend the prefix form to capture such
visual attributes -hence the name quasi/-prefix.

[figure69]Figure 1: A math object with attributes. Each
of the attributes themselves contain math objects.

A key feature of the quasi-prefix form is that it delays the
assignment of semantic interpretation to instances of ambiguous
written mathematics. At the same time, it is sufficiently rich
to permit renderings that are independent of the order in which
the written symbols would appear on paper. Linear renderings
with the rendering-order hard-coded into the system can be
produced with a simpler representation, e.g.,a linear
list, or even the TeX encoding itself. This was shown by
TeXTALK , a string-substitution based program that directly
transformed TeX source to produce spoken renderings [Ram92][Ram91].

As an example, assume that \kronecker[+] is defined as an infix binary
operator. Given the expression

[displaymath327]

encoded as

[LVerbatim86]

we can represent it in the quasi-prefix form by a tree whose
root is object kronecker, and write rendering rules
for object kronecker/ that produce either ``a
kronecker product b'', or ``kronecker product of a and b''. The
former rendering can be produced by TeXTALK as well, but a
simpler list-like representation restricts the system to this
one form of rendering.

In producing printed output, one view is sufficient; once
the information has been presented visually, a person reading
the material can access it in any desired order. But even with
visual rendering, different views may be desired. For example,
one may wish a view that gives only the table of contents of a
paper. Or, for a document that presents an algorithm, one view
could give the whole presentation and a second view could
present only the overview of the algorithm. See [Lam93] for a discussion
on the hierarchical presentation of proofs. The linearity of
audio makes it essential that AsTeR have the ability to present
multiple views. Lack of this feature is one of the major
shortcomings of books on tape, where the listener is restricted
to the one view presented by the person speaking the text.
AsTeR allows the listener to explore the material the same as a
person perusing printed material, and thereby enables
active/ listening.